Your AC suffers if that fan doesn't work. If you want to test just the fan, since you have to remove it anyway. After you get it out you'll see three wires in it's plug (the plug is behind the fan...). The brown wire is the ground, the blue wire is the high speed feed, the black/blue wire is the normal speed feed wire. Connect the brown wire's pin to a good ground then just touch a 12v source wire to either of the other wires and the fan should come on, either low speed or high speed depending on which wire you choose. If the fan works then the problem could be the two relays ( normal / high ).
Let me know what you find.

I got a cheapo fan from eBay last year and then it just broke on my while driving on the highway. The metal at the center got worn out. This was in a matter of two months after installation.

Get the good stuff. I think this is one area in which it is worth doing. I also thought, "Well, it is just a fan and an electric motor. Anybody can do that right." Pelican parts has them for $260. That is the lowest price I have seen on the web for that fan.